I have been arguing for a long time (see here or here) that changes in family structure over time distort the measurement of income growth and inequality. The basic problem is that using measures such as average income or per capita GDP may not be good measures of how the well-being of the average person has changed over time–high earners can pull up the mean while the average person makes no progress. So you use the median. But the median has its own problems, a fact systematically ignored by those with an ax to grind. The problem with the median is that it’s difficult to compare changes in standard of living over time when there are large changes in the population or the structure of the population over time.

So for example, if there is immigration and if new immigrants have lower incomes than the existing population, the median will fall even if everyone else’s income hasn’t changed. The new immigrants are expanding the left-hand tail of the population pulling the median down. The median falls, but that tells you nothing about what happened to the well-being of the person who was at the median income before the immigration occurred.

Similarly, if there is an increase in divorce, then there is an increase in the number of households and the number of families independent of population growth. Suppose there is a couple where both husband and wife work. After the divorce, one household becomes two. If the husband and the wife each on their own earned more than the median, then median household income rises–the original household was above the median and now there are two households above the median. But if one of the members earns less than the median then we’re adding an additional household below the median. Or if the husband worked before the divorce and earned more than the median while the wife worked at home. After the divorce, if the wife enters the labor force and earns less than the median household income, then the median falls.

In theory, this effect could go either way. But in fact, there is an enormous difference in divorce rates by income. Poorer men are much more likely to get divorced than richer men. See here (and scroll down to the chart titled “Change in Marriage and Earnings of Men, 1970-2011.” Poorer families are more likely to divorce than richer families. See here, first chart.

So some portion of the increase in inequality is not an increase in outcomes due to the nature of the economic process but due to how measuring inequality is affected by divorce. Now some sociologists are actually measuring the impact. Jason Parle at Economix at the NYT reports:

As my article this weekend about two families in Ann Arbor, Mich., points out, the widening in many measures of inequality can be traced in part to changes in marriage patterns, rather than just changes in individual earnings. A number of scholars have looked at the varied dimensions of this thesis — growing inequality, changes in family structure, and the connection between the two. Here is a look at some of their findings.

On inequality:An interesting pattern over the last four decades is that inequality has grown much faster for households with children than it has for households over all — an indication that changes in family structure (as opposed to wages and employment alone) have increased inequality.

Bruce Western and Tracey Shollenberger of the Harvard sociology department compared households at the 90th percentile and the 10th percentile. In 1970, the top households had 8.9 times the income of the bottom. By 2011 they had nearly 11.7 times as much — inequality between them grew 31 percent.

But among households with children it grew 121 percent. (The ratio went from 4.8 in 1970 to 10.6 last year.)

He then presents this graph from Western and Shollenberger:

It’s not the greatest graph–there’s no scale provided on the vertical axis. But you can figure it out from the notations on the graph. The vertical axis is measured in multiples. Each horizontal line represents 2 times the ratio of the 90th to the 10th percentile. So in 1970, among households with children, the 90th percentile earned 4.8 times the 10th percentile. As time passed, that ratio increased pretty relentlessly so that by about 1993, the families in the 90th percentile earned over ten times what the households in the bottom 10% earned. The ratio then fell for a while almost dropping to a multiple of eight.

Over that same time period, the ratio between the 90th percentile and the 10th percentile rose for all households, but not nearly as much. It rose from a multiple of 8.9 to a multiple of maybe 10.5. A much smaller increase. And that includes the households with children. If we just looked at the households without children, the increase would smaller still and might not even increase at all.

As Parle puts it:

An interesting pattern over the last four decades is that inequality has grown much faster for households with children than it has for households over all — an indication that changes in family structure (as opposed to wages and employment alone) have increased inequality.

There are two reasons why family structure might affect inequality. The first reason is the one I gave above–a change in measured inequality that says little or nothing about the how the economy is working but rather reflects a statistical artifact. So for example, if high income households with children tend to stay married while low-income parents have a higher (and increasing) divorce rate, then you will see new households created that fall into the bottom half of the distribution and some of them may fall into the bottom 10%. It is possible that no one has any smaller command over goods and services relative to what they had before, but measured inequality will rise.

The second possibility is that there are inherent economic disadvantages to being divorced with children or unmarried with children. In this story, the rise in single parenthood doesn’t just create statistical artifacts. Raising a child without a spouse is very challenging. There are no economies of scale and the single parent may have to take lower-paying jobs that are sufficiently flexible to allow for parenting while single.

In both of these cases changes in family structure lead to increasing inequality, but it is the social forces that are driving the inequality rather than differential returns to low and high skill embedded in the economy.

Parle then mentions three different studies of how much of the change in family structure might account for the measured change in inequality:

Changes in family structure may explain anywhere from 15 to 40 percent of the increased inequality in recent decades. Readers may wonder why there is such a broad range of estimates. It depends on the time period examined, the income rungs examined, and assumptions about how much the absent parent might have brought into the household.

Mr. Western’s estimate that the rise in single parenthood explains 21 percent of the growth in inequality comes from a 2008 article in the American Sociological Review (with Christine Percheski and Deirdre Bloom). He examined the change from 1975 to 2005.

Gary Burtless looked at different years (1979 to 1996) for the European Economic Review but came up with the same figure: 21 percent. He also found that the increased tendency of educated people to marry each other accounted for another 13 percent of inequality’s growth.

The other estimate cited in the article comes from Robert Lerman of the Urban Institute. His unpublished analysis examines families with children at the 25th percentile and the 75th percentile. In 1975, the higher group had 2.16 times the income of the lower group. By 2008, it had risen to 3.09. Mr. Lerman estimated that 40 percent of that rise was the result of increasing single parenthood.

A quick look at these papers suggests that they are not concerned with the statistical artifact problem. They are simply noting the correlation between being a single parent and being poor. They are not trying to figure out which way the causation runs–whether being a single parent makes it harder to hold down a good job or whether people who get good jobs are less likely to be single parents.

Either way, the measured increases in inequality misstates how the economy has rewarded high skills vs. low skills over the last forty years.